What is the integral of 5*4^x ?

The integral of 5*4^x is (5*2^{2x-1})/(ln(2))+C

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integral of 5*4^x

\int 5 \cdot 4^{x} d x

\frac{5 \cdot 2 ^{2 x - 1}}{ln ( 2 )} + C

Solution steps

\int 5 \cdot 4^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int 4^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 5 \cdot \frac{4 ^{x}}{ln ( 4 )}

Simplify

5 \cdot \frac{4 ^{x}}{ln ( 4 )} : \frac{5 \cdot 2 ^{2 x - 1}}{ln ( 2 )}

= \frac{5 \cdot 2 ^{2 x - 1}}{ln ( 2 )}

Add a constant to the solution

= \frac{5 \cdot 2 ^{2 x - 1}}{ln ( 2 )} + C